Best $m$-term trigonometric approximations of the isotropic Nikol'skii-Besov-type classes of periodic functions of several variables

Abstract

We obtained the exact order estimates of the best $m$-term trigonometric approximations of the isotropic Nikol'skii-Besov-type classes $B^{\omega}_{p,\theta}$ of periodic functions of several variables in the spaces $B_{q,1}$ for $1<p<q<\infty$, $q\geq 2$. A peculiarity of these spaces, as linear subspaces of $L_q$, is that the norm in them is stronger than the $L_q$-norm. It was found that the obtained estimates of the considered approximation characteristic coincide in order with the estimates of the corresponding characteristic of the classes $B^{\omega}_{p,\theta}$ in the spaces $L_q$.